1.) Prove that A(B + C) = AB + AC for 2 x 2 matrices B and C and a 1 x 2 matrix A. 2.) Find the inverse of A = 2 3 -1 3.) Determine whether the following matrices are nilpotent: 12 -9 16 -12 Extension: can you determine a pattern in these two matrices? 4.) Factorise the following: 7GX - X X2 - 2XY + Yz 5.) Solve the following: 6. ) Prove the cancellation law: rA = rB - A = B (r # 0), TA = SA - r=s (A #0)